Higher representation infinite algebras from McKay quivers of metacyclic groups

Abstract

For each prime number s we introduce examples of (s − 1)-and s-representation infinite algebras in the sense of Herschend, Iyama and Oppermann, which arise from skew group algebras of some metacyclic groups embedded in SL(s, C) and SL(s + 1, C). For this purpose, we give a description of the McKay quiver with a superpotential of such groups. Moreover we show that for s = 2 our examples correspond to the classical tame hereditary algebras of typeD.2010 Mathematics Subject Classification. 16G20; 16S35; 16E65.

Skew group algebras of Jacobian algebras

“…We show that G-invariant cuts on (Q, W ) induce cuts on (Q G , W G ), and the corresponding truncated Jacobian algebras are obtained from each other by a skew group algebra construction. Thus we have that, under some hypotheses, 2-representation finiteness is preserved under taking skew group algebras (note that an analogous result was obtained, using different methods, for some d-representation infinite algebras in [Gio19]). Moreover we give some sufficient conditions on (Q, W ) which imply that all the truncated Jacobian algebras of (Q G , W G ) are derived equivalent.…”